Plot the enthalpy of combustion for gaseous methane (CH4),

Ten grams of propane (\(\mathrm{C}_{3} \mathrm{H}_{8}\)) burns with just enough oxygen (\(\mathrm{O}_{2}\)) for complete combustion. Determine the amount of oxygen required and the amount of combustion products formed, each in grams.

Ethane (\(\mathrm{C}_{2} \mathrm{H}_{6}\)) burns completely with the theoretical amount of air. Determine the air–fuel ratio on a (a) molar basis, (b) mass basis.

A gas turbine burns octane (\(\mathrm{C}_{8} \mathrm{H}_{18}\)) completely with 400% of theoretical air. Determine the amount of \(\mathrm{N}_{2}\) in the products, in kmol per kmol of fuel.

A closed, rigid vessel initially contains a mixture of 40% CO and 60% \(\mathrm{O}_{2}\) on a mass basis. These substances react giving a final mixture of \(\mathrmCO}_{2}\) and \(\mathrm{O}_{2}\). Determine the balanced reaction equation.

One hundred kmol of propane (\(\mathrm{C}_{3} \mathrm{H}_{8}\)) together with 3572 kmol of air enter a furnace per unit of time. Carbon dioxide, carbon monoxide, and unburned fuel appear in the products of combustion exiting the furnace. Determine the percent excess or percent deficiency of air, whichever is appropriate.

Propane (\(\mathrm{C}_{3} \mathrm{H}_{8}\)) is burned with air. For each case, obtain the balanced reaction equation for complete combustion (a) with the theoretical amount of air. (b) with 20% excess air. (c) with 20% excess air, but only 90% of the propane being consumed in the reaction.

Butane (\(\mathrm{C}_{4} \mathrm{H}_{10}\)) burns completely with air. The equivalence ratio is 0.9. Determine (a) the balanced reaction equation. (b) the percent excess air.

A natural gas mixture having a molar analysis 60% \(\mathrm{CH}_{4}\), 30% \(\mathrm{C}_{2} \mathrm{H}_{6}\), 10% \(\mathrm{N}_{2}\) is supplied to a furnace like the one shown in Fig. P13.8, where it burns completely with 20% excess air. Determine (a) the balanced reaction equation. (b) the air–fuel ratio, both on a molar and a mass basis.

A fuel mixture with the molar analysis 70% \(\mathrm{CH}_{4}\), 20% CO, 5% \(\mathrm{O}_{2}\), and 5% \(\mathrm{N}_{2}\) burns completely with 20% excess air. Determine (a) the balanced reaction equation. (b) the air–fuel ratio, both on a molar and mass basis.

A gas mixture with the molar analysis 25% \(\mathrm{H}_{2}\), 25% CO, 50% \(\mathrm{O}_{2}\) reacts to form products consisting of \(\mathrm{CO}_{2}\), \(\mathrm{H}_{2} \mathrm{O}\), and \(\mathrm{O}_{2}\) only. Determine the amount of each product, in kg per kg of mixture.

A natural gas with the molar analysis 94.4% \(\mathrm{CH}_{4}\), 3.4% \(\mathrm{C}_{2} \mathrm{H}_{6}\), 0.6% \(\mathrm{C}_{3} \mathrm{H}_{8}\), 0.5% \(\mathrm{C}_{4} \mathrm{H}_{10}), 1.1% \(\mathrm{N}_{2}\) burns completely with 20% excess air in a reactor operating at steady state. If the molar flow rate of the fuel is 0.1 kmol/h, determine the molar flow rate of the air, in kmol/h.

A natural gas fuel mixture has the molar analysis shown below. Determine the molar analysis of the products for complete combustion with 70% excess dry air.

Coal with the mass analysis 79.2% C, 5.7% \(\mathrm{H}_{2}\), 10% \(\mathrm{O}_{2}\), 1.5% \(\mathrm{N}_{2}\), 0.6% S, 3% noncombustible ash burns completely with the theoretical amount of air. Determine (a) the air–fuel ratio on a mass basis. (b) the amount of \(\mathrm{SO}_{2}\) produced, in kg per kg of coal.

A coal sample has a mass analysis of 80.4% carbon, 3.9% hydrogen (\(\mathrm{H}_{2}\)), 5.0% oxygen (\(\mathrm{O}_{2}\)), 1.1% nitrogen (\(\mathrm{N}_{2}\)), 1.1% sulfur, and the rest is noncombustible ash. For complete combustion with 120% of the theoretical amount of air, determine (a) the air–fuel ratio on a mass basis, (b) the amount of \(\mathrm{SO}_{2}\) produced, in kg per kg of coal.

A sample of dried feedlot manure is being tested for use as a fuel. The mass analysis of the sample is 42.7% carbon, 5.5% hydrogen (\(\mathrm{H}_{2}\)), 31.3% oxygen (\(\mathrm{O}_{2}\)), 2.4% nitrogen (\(\mathrm{N}_{2}\)), 0.3% sulfur, and 17.8% noncombustible ash. The sample is burned completely with 120% of theoretical air. Determine (a) the balanced reaction equation. (b) the air–fuel ratio on a mass basis.

A sample of dried Appanoose County coal has a mass analysis of 71.1% carbon, 5.1% hydrogen (\(\mathrm{H}_{2}\)), 9.0% oxygen (\(\mathrm{O}_{2}\)), 1.4% nitrogen (\(\mathrm{N}_{2}\)), 5.8% sulfur, and the rest noncombustible ash. For complete combustion with the theoretical amount of air, determine (a) the amount of \(\mathrm{SO}_{2}\) produced, in kg per kg of coal. (b) the air–fuel ratio on a mass basis.

Dodecane (\(\mathrm{C}_{12} \mathrm{H}_{26}\)) burns completely with 150% of theoretical air. Determine (a) the air–fuel ratio on a molar and mass basis. (b) the dew point temperature of the combustion products, in \({ }^{\circ} \mathrm{C}\), when cooled at 1 atm.

Butane (\(\mathrm{C}_{4} \mathrm{H}_{10}\)) burns completely with 150% of theoretical air. If the combustion products are cooled at 1 atm to temperature T, plot the amount of water vapor condensed, in kmol per kmol of fuel, versus T ranging from 20 to \(60^{\circ} \mathrm{C}\).

Ethylene (\(\mathrm{C}_{2} \mathrm{H}_{4}\)) burns completely with air and the combustion products are cooled to temperature T at 1 atm. The air–fuel ratio on a mass basis is AF. (a) Determine for AF = 15 and \(T=70^{\circ} \mathrm{F}\), the percent excess air and the amount of water vapor condensed, in lb per lbmol of fuel. (b) Plot the amount of water vapor condensed, in lb per lbmol of fuel, versus T ranging from 70 to \(100^{\circ} \mathrm{F}\), for AF = 15, 20, 25, 30.

A gaseous fuel mixture with a specified molar analysis burns completely with moist air to form gaseous products as shown in Fig. P13.20. Determine the dew point temperature of the products, in \({ }^{\circ} \mathrm{C}\).

The gas driven off when low-grade coal is burned with insufficient air for complete combustion is known as producer gas. A particular producer gas has the following volumetric analysis: 3.8% \(\mathrm{CH}_{4}, 0.1 \% \mathrm{C}_{2} \mathrm{H}_{6}, 4.8 \% \mathrm{CO}_{2}, 11.7 \% \mathrm{H}_{2}\), 0.6% \(\mathrm{O}_{2}\), 23.2% CO, and the remainder \(\mathrm{N}_{2}\). For complete combustion with the theoretical amount of air, determine (a) the molar analysis of the dry products of combustion. (b) the amount of water vapor condensed, in lbmol/lbmol of producer gas, if the products are cooled to \(70^{\circ} \mathrm{F}\) at a constant pressure of 1 atm.

Propane (\(\mathrm{C}_{3} \mathrm{H}_{8}\)) burns completely with 180% of theoretical air entering at \(40^{\circ} \mathrm{C}\), 1 atm, 60% relative humidity. Obtain the balanced reaction equation, and determine the dew point temperature of the products, in \({ }^{\circ} \mathrm{C}\), when cooled at 1 atm.

Butane (\(\mathrm{C}_{4} \mathrm{H}_{10}\)) burns completely with 160% of theoretical air at \(20^{\circ} \mathrm{C}\), 1 atm, and 90% relative humidity. Determine (a) the balanced reaction equation. (b) the dew point temperature, in \({ }^{\circ} \mathrm{C}\), of the products, when cooled at 1 atm.

Methane (\(\mathrm{CH}_{4}\)) enters a furnace and burns completely with 150% of theoretical air entering at \(25^{\circ} \mathrm{C}\), 0.945 bar, 75% relative humidity. Determine (a) the balanced reaction equation. (b) the dew point temperature of the combustion products, in \({ }^{\circ} \mathrm{C}\), when cooled at 0.945 bar.

Propane (\(\mathrm{C}_{3} \mathrm{H}_{8}\)) burns completely with the theoretical amount of air at \(60^{\circ} \mathrm{F}\), 1 atm, 90% relative humidity. Determine (a) the balanced reaction equation. (b) the dew point temperature of the combustion products at 1 atm. (c) the amount of water condensed, in lbmol per lbmol of fuel, if the combustion products are cooled to \(75^{\circ} \mathrm{F}\), at 1 atm.

A liquid fuel mixture that is 40% octane (\(\mathrm{C}_{8} \mathrm{H}_{18}\)) and 60% decane (\(\mathrm{C}_{10} \mathrm{H}_{22}\)) by mass is burned completely with 10% excess air at \(25^{\circ} \mathrm{C}\), 1 atm, 80% relative humidity. (a) Determine the equivalent hydrocarbon composition, \(\mathrm{C}_{a} \mathrm{H}_{b}\), of a fuel that would have the same carbon–hydrogen ratio on a mass basis as the fuel mixture. (b) If the combustion products are cooled to \(25^{\circ} \mathrm{C}\) at a pressure of 1 atm, determine the amount of water vapor that condenses, in kg per kg of fuel mixture.

Hydrogen (\(\mathrm{H}_{2}\)) enters a combustor with a mass flow rate of 2 kg/h and burns with air entering at \(30^{\circ} \mathrm{C}\), 1 atm with a volumetric flow rate of \(120 \mathrm{~m}^{3} / \mathrm{h}\). Determine the percent of theoretical air used.

Methyl alcohol (\(\mathrm{CH}_{3} \mathrm{OH}\)) burns with 200% theoretical air, yielding \(\mathrm{CO}_{2}\), \(\mathrm{H}_{2} \mathrm{O}\), \(\mathrm{O}_{2}\), and \(\mathrm{N}_{2}\). Determine the (a) balanced reaction equation. (b) air–fuel ratio on a mass basis. (c) molar analysis of the products.

Octane (\(\mathrm{C}_{8} \mathrm{H}_{18}\)) is burned with 20% excess air, yielding \(\mathrm{CO}_{2}\), CO, \(\mathrm{O}_{2}\), \(\mathrm{H}_{2} \mathrm{O}\), and \(\mathrm{N}_{2}\) only. If 5% of the dry products (molar basis) is \(\mathrm{O}_{2}\), determine (a) the balanced reaction equation. (b) the analysis of the products on a dry molar basis.

Hexane (\(\mathrm{C}_{6} \mathrm{H}_{14}\)) burns with dry air to give products with the dry molar analysis 8.5% \(\mathrm{CO}_{2}\), 5.2% CO, 3% \(\mathrm{O}_{2}\), 83.3% \(\mathrm{N}_{2}\), Determine (a) the balanced reaction equation. (b) the percent of theoretical air. (c) the dew point temperature, in \({ }^{\circ} \mathrm{C}\), of the products at 1 atm.

The components of the exhaust gas of a spark-ignition engine using a fuel mixture represented as \(\mathrm{C}_{8} \mathrm{H}_{17}\) have a dry molar analysis of 8.7% \(\mathrm{CO}_{2}\), 8.9% CO, 0.3% \(\mathrm{O}_{2}\), 3.7% \(\mathrm{H}_{2}\), 0.3% \(\mathrm{CH}_{4}\), and 78.1% \(\mathrm{N}_{2}\). Determine the equivalence ratio.

The combustion of a hydrocarbon fuel, represented as \(\mathrm{C}_{a} \mathrm{H}_{b}\), results in products with the dry molar analysis 11% \(\mathrm{CO}_{2}\), 0.5% CO, 2% \9\mathrm{CH}_{4}\), 1.5% \(\mathrm{H}_{2}), 6% \(\mathrm{O}_{2}\), and 79% \(\mathrm{N}_{2}\). Determine the air–fuel ratio on (a) a molar basis, (b) a mass basis.

Decane (\(\mathrm{C}_{10} \mathrm{H}_{22}\)) burns completely in dry air. The air– fuel ratio on a mass basis is 33. Determine the (a) analysis of the products on a dry molar basis. (b) percent of theoretical air.

Butane (\(\mathrm{C}_{4} \mathrm{H}_{10}\)) burns with air, giving products having the dry molar analysis 11.0% \(\mathrm{CO}_{2}\), 1.0% CO, 3.5% \(\mathrm{O}_{2}\), 84.5% \(\mathrm{N}_{2}\). Determine (a) the percent of theoretical air. (b) the dew point temperature of the combustion products, in \({ }^{\circ} \mathrm{C}\), at 1 bar.

A natural gas with the volumetric analysis 97.3% \(\mathrm{CH}_{4}\), 2.3% \(\mathrm{CO}_{2}\), 0.4% \(\mathrm{N}_{2}\) is burned with air in a furnace to give products having a dry molar analysis of 9.20% \(\mathrm{CO}_{2}\), 3.84% \(\mathrm{O}_{2}\), 0.64% CO, and the remainder \(\mathrm{N}_{2}\). Determine (a) the percent theoretical air. (b) the dew point temperature, in \({ }^{\circ} \mathrm{F}\), of the combustion products at 1 atm.

A fuel oil having an analysis on a mass basis of 85.7% C, 14.2% H, 0.1% inert matter burns with air to give products with a dry molar analysis of 12.29% \(\mathrm{CO}_{2}\), 3.76% \(\mathrm{O}_{2}\), 83.95% \(\mathrm{N}_{2}\). Determine the air–fuel ratio on a mass basis.

Methanol (\(\mathrm{CH}_{3} \mathrm{OH}\)) burns with air. The product gas is analyzed and the laboratory report gives only the following percentages on a dry molar basis: 7.1% \(\mathrm{CO}_{2}\), 2.4% CO, 0.84% (\(\mathrm{CH}_{3} \mathrm{OH}\). Assuming the remaining components consist of \(\mathrm{O}_{2}\) and \(\mathrm{N}_{2}\), determine (a) the percentages of \(\mathrm{O}_{2}\) and \(\mathrm{N}_{2}\) in the dry molar analysis. (b) the percent excess air.

A fuel oil with the mass analysis 87% C, 11% H, 1.4% S, 0.6% inert matter burns with 120% of theoretical air. The hydrogen and sulfur are completely oxidized, but 95% of the carbon is oxidized to \(\mathrm{CO}_{2}\) and the remainder to CO. (a) Determine the balanced reaction equation. (b) For the CO and \(\mathrm{SO}_{2}\), determine the amount, in kmol per 106 kmol of combustion products (that is, the amount in parts per million).

Pentane (\(\mathrm{C}_{5} \mathrm{H}_{12}\)) burns with air so that a fraction x of the carbon is converted to \(\mathrm{CO}_{2}\). The remaining carbon appears as CO. There is no free \(\mathrm{O}_{2}\) in the products. Develop plots of the air–fuel ratio and the percent of theoretical air versus x, for x ranging from zero to unity.

For each of the following mixtures, determine the equivalence ratio and indicate if the mixture is lean or rich: (a) 1 lbmol of methane (\(\mathrm{CH}_{4}\)) and 8 lbmol of air. (b) 1 kg of ethane (\\mathrm{C}_{2} \mathrm{H}_{6}\)) and 17.2 kg of air.

Methyl alcohol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) burns in dry air according to the reaction \(\begin{aligned} \mathrm{CH}_{3} \mathrm{OH} & +3.3\left(\mathrm{O}_{2}+3.76 \mathrm{~N}_{2}\right) \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O} \\ & +1.8 \mathrm{O}_{2}+12.408 \mathrm{~N}_{2} \end{aligned}\) Determine the (a) air–fuel ratio on a mass basis. (b) equivalence ratio. (c) percent excess air.

Ethyl alcohol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) burns in dry air according to the reaction \(\begin{aligned} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} & +2.16\left(\mathrm{O}_{2}+3.76 \mathrm{~N}_{2}\right) \rightarrow 0.32 \mathrm{CO}_{2}+1.68 \mathrm{CO} \\ & +3 \mathrm{H}_{2} \mathrm{O}+8.1216 \mathrm{~N}_{2} \end{aligned}\) Determine the (a) air–fuel ratio on a mass basis. (b) equivalence ratio. (c) percent theoretical air.

Octane (\(\mathrm{C}_{8} \mathrm{H}_{18}\)) enters an engine and burns with air to give products with the dry molar analysis of \(\mathrm{CO}_{2}\), 10.5%; CO, 5.8%; \(\mathrm{CH}_{4}\), 0.9%; \(\mathrm{H}_{2}), 2.6%; \(\mathrm{O}_{2}\), 0.3%; \(\mathrm{N}_{2}\), 79.9%. Determine the equivalence ratio.

Figure P13.44 shows four components in series. Coal, oxygen (\(\mathrm{O}_{2}\)), and steam are fed to the gasifier, which produces syngas (synthesis gas) with the following molar analysis: \(\begin{array}{l} \mathrm{CH}_{4}, 0.3 \% ; \mathrm{H}_{2}, 29.6 \% ; \mathrm{CO}_{2}, 10.0 \% ; \mathrm{CO}, 41.0 \% ; \\ \mathrm{N}_{2}, 0.8 \% ; \mathrm{H}_{2} \mathrm{O}, 17.0 \%, \mathrm{H}_{2} \mathrm{~S}, 1.1 \%, \mathrm{NH}_{3}, 0.2 \% \mid \end{array}\) The \(\mathrm{H}_{2} \mathrm{S}\) and \(\mathrm{NH}_{3}\) are removed and the mixture then passes through a chiller that condenses 98% of the water present in the syngas stream. The condensate is removed and the resulting gas stream is fed to the combustor, where its burns completely with 400% of theoretical air. For the combustor, determine the amount of air required, in kmol per kmol of syngas.

Liquid octane (\(\mathrm{C}_{8} \mathrm{H}_{18}\)) at \(77^{\circ} \mathrm{F}\), 1 atm enters a combustion chamber operating at steady state and burns completely with 50% excess dry air entering at \(120^{\circ} \mathrm{F}\), 1 atm. The products exit at \(1060^{\circ} \mathrm{F}\), 1 atm. Determine the rate of heat transfer between the combustion chamber and its surroundings, in Btu per lbmol of fuel entering. Kinetic and potential energy effects are negligible.

Propane (\(\mathrm{C}_{3} \mathrm{H}_{8}\)) at 298 K, 1 atm, enters a combustion chamber operating at steady state with a molar flow rate of 0.7 kmol/s and burns completely with 200% of theoretical air entering at 298 K, 1 atm. Kinetic and potential energy effects are negligible. If the combustion products exit at 560 K, 1 atm, determine the rate of heat transfer for the combustion chamber, in kW. Repeat for an exit temperature of 298 K.

Methane (\(\mathrm{CH}_{4}\)) at \(25^{\circ} \mathrm{C}\), 1 atm enters a furnace operating at steady state and burns completely with 140% of theoretical air entering at 400 K, 1 atm. The products of combustion exit at 700 K, 1 atm. Kinetic and potential energy effects are negligible. If the rate of heat transfer from the furnace to the surroundings is 400 kW, determine the mass flow rate of methane, in kg/s.

Methane gas (\(\mathrm{CH}_{4}\)) at \(25^{\circ} \mathrm{C}\), 1 atm and a volumetric flow rate of \(27 \mathrm{~m}^{3} / \mathrm{h}\) enters a heat-treating furnace operating at steady state. The methane burns completely with 140% of theoretical air entering at \(127^{\circ} \mathrm{C}\), 1 atm. Products of combustion exit at \(427^{\circ} \mathrm{C}\), 1 atm. Determine (a) the volumetric flow rate of the air, in \(\mathrm{m}^{3} / \mathrm{h}\). (b) the rate of heat transfer from the furnace, in kJ/h.

Liquid ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) at \(77^{\circ} \mathrm{F}\), 1 atm enters a combustion chamber operating at steady state and burns completely with dry air entering at \(40^{\circ} \mathrm{F}\), 1 atm. The fuel flow rate is 50 lb/s, and the equivalence ratio is 0.8. Products of combustion exit at \(2000^{\circ} \mathrm{F}\), 1 atm. Ignoring kinetic and potential energy effects, determine (a) the air–fuel ratio on a mass basis. (b) the rate of heat transfer, in Btu/s.

Octane gas (\(\mathrm{C}_{8} \mathrm{H}_{18}\)) at 25C, 1 atm enters a combustion chamber operating at steady state and burns with 120% theoretical air entering at \(25^{\circ} \mathrm{C}\), 1 atm. The combustion products exit at 1200 K and include only \(\mathrm{CO}_{2}\), \(\mathrm{H}_{2} \mathrm{O}\), \(\mathrm{O}_{2}\), and \(\mathrm{N}_{2}\). If the rate of heat transfer from the combustion chamber to the surroundings is 2500 kW, determine the mass flow rate of the fuel, in kg/s.

Liquid propane (\(\mathrm{C}_{3} \mathrm{H}_{8}\)) at \(25^{\circ} \mathrm{C}\), 1 atm, enters a wellinsulated reactor operating at steady state. Air enters at the same temperature and pressure. For liquid propane, \(\bar{h}_{\mathrm{f}}^{\circ}=-118,900 \mathrm{~kJ} / \mathrm{kmol}\). Determine the temperature of the combustion products, in K, for complete combustion with (a) the theoretical amount of air. (b) 300% of theoretical air.

The energy required to vaporize the working fluid passing through the boiler of a simple vapor power plant is provided by the complete combustion of methane with 110% of theoretical air. The fuel and air enter in separate streams at \(25^{\circ} \mathrm{C}\), 1 atm. Products of combustion exit the stack at \(150^{\circ} \mathrm{C}\), 1 atm. Plot the mass flow rate of fuel required, in kg/h per MW of power developed by the plant versus the plant thermal efficiency, \(\eta\). Consider \(\eta) in the range 30–40%. Kinetic and potential energy effects are negligible.

Liquid octane (\(\mathrm{C}_{8} \mathrm{H}_{18}\)) at \(25^{\circ} \mathrm{C}\), 1 atm enters the combustor of a simple open gas turbine power plant and burns completely with 400% of theoretical air entering the compressor at \(25^{\circ} \mathrm{C}\), 1 atm. Products of combustion exit the turbine at \(627^{\circ} \mathrm{C}\), 1 atm. The rate of heat transfer from the gas turbine is estimated as 15% of the net power developed. Determine the net power developed, in kJ per kmol of fuel. Kinetic and potential energy effects are negligible.

Octane gas \(\mathrm{C}_{8} \mathrm{H}_{18}\) at \(25^{\circ} \mathrm{C}\) enters a jet engine and burns completely with 300% of theoretical air entering at \(25^{\circ} \mathrm{C}\), 1 atm with a volumetric flow rate of \(42 \mathrm{~m}^{3} / \mathrm{s}\). Products of combustion exit at 990 K, 1 atm. If the fuel and air enter with negligible velocities, determine the velocity of the exiting combustion products, in m/s. Neglect heat transfer between the engine and its surroundings.

Propane gas (\(\mathrm{C}_{3} \mathrm{H}_{8}\)) at \(25^{\circ} \mathrm{C}\), 1 atm enters a reactor operating at steady state and burns with 20% excess air entering at \(25^{\circ} \mathrm{C}\), 1 atm. Of the carbon entering with the fuel, 94% (molar basis) appears in the products as \(\mathrm{CO}_{2}\) and the rest as CO. Heat transfer from the reactor occurs at a rate of 1.4 3 106 kJ per kmol of propane. Ignoring kinetic and potential energy effects, determine the temperature of the combustion products exiting the reactor, in K.

One lbmol of octane gas (\(\mathrm{C}_{8} \mathrm{H}_{18}\)) reacts with the theoretical amount of air in a closed, rigid tank. Initially, the reactants are at \(77^{\circ} \mathrm{F}\), 1 atm. After complete combustion, the pressure in the tank is 3.98 atm. Determine the heat transfer, in Btu.

A closed, rigid vessel initially contains a gaseous mixture at \(25^{\circ} \mathrm{C}\), 1 atm with the molar analysis of 20% ethane (\(\mathrm{C}_{2} \mathrm{H}_{6}\)), 80% oxygen (\(\mathrm{O}_{2}\)). The initial mixture contains one kmol of ethane. Complete combustion occurs, and the products are cooled to \(25^{\circ} \mathrm{C}\). Determine the heat transfer, in kJ, and the final pressure, in atm.

A mixture of 1 kmol of hydrogen (\(\mathrm{H}_{2}\)) and n kmol of oxygen (\(\mathrm{O}_{2}\)), initially at \(25^{\circ} \mathrm{C}\) and 1 atm, burns completely in a closed, rigid, insulated container. The container finally holds a mixture of water vapor and \(\mathrm{O}_{2}\) at 3000 K. The ideal gas model applies to each mixture and there is no change in kinetic or potential energy between the initial and final tates. Determine (a) the value of n. (b) the final pressure, in atm.

Calculate the enthalpy of combustion of gaseous pentane (\(\mathrm{C}_{5} \mathrm{H}_{12}\)), in kJ per kmol of fuel, at \(25^{\circ} \mathrm{C}\) with water vapor in the products.

Plot the enthalpy of combustion for gaseous propane (\(\mathrm{C}_{3} \mathrm{H}_{8}\)), in Btu per lbmol of fuel, at 1 atm versus temperature in the interval 77 to \(500^{\circ} \mathrm{F}\). Assume water vapor in the products. For propane, let \(c_{p}=0.41 \mathrm{Btu} / \mathrm{lb} \cdot{ }^{\circ} \mathrm{R}\).

Plot the enthalpy of combustion for gaseous methane (\(\mathrm{CH}_{4}\)), in Btu per lbmol of fuel, at 1 atm versus temperature in the interval from 537 to \(1800^{\circ} \mathrm{R}\). Assume water vapor in the products. For methane, let \(\bar{c}_{p}=4.52+7.37(T / 1000)\) \(\text { Btu/lbmol } \cdot{ }^{\circ} \mathrm{R}\), where T is in \({ }^{\circ} \mathrm{R}\).

Determine the lower heating value, in kJ per kmol of fuel and in kJ per kg of fuel, at \(25^{\circ} \mathrm{C}\), 1 atm for (a) gaseous ethane (\(\mathrm{C}_{2} \mathrm{H}_{6}\)). (b) liquid ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)). (c) gaseous propane (\(\mathrm{C}_{3} \mathrm{H}_{8}\)). (d) liquid octane (\(\mathrm{C}_{8} \mathrm{H}_{18}\)).

Liquid octane (\(\mathrm{C}_{8} \mathrm{H}_{18}\)) at \(77^{\circ} \mathrm{F}\), 1 atm enters an insulated reactor operating at steady state and burns completely with 400% of theoretical air entering at \(77^{\circ} \mathrm{F}\), 1 atm. Determine the temperature of the exiting combustion products, in \({ }^{\circ} \mathrm{R}\). Neglect kinetic and potential energy effects.

Methane (\(\mathrm{CH}_{4}\)) at \(25^{\circ} \mathrm{C}\), 1 atm enters an insulated reactor operating at steady state and burns with the theoretical amount of air entering at \(25^{\circ} \mathrm{C}\), 1 atm. Determine the temperature of the exiting combustion products, in K, if 90% of the carbon in the fuel burns to \(\mathrm{CO}_{2}\) and the rest to CO. Neglect kinetic and potential energy effects.

Liquid octane (\(\mathrm{C}_{8} \mathrm{H}_{18}\)) at \(25^{\circ} \mathrm{C}\), 1 atm enters an insulated reactor operating at steady state and burns with 90% of theoretical air at \(25^{\circ} \mathrm{C}\), 1 atm to form products consisting of \(\mathrm{CO}_{2}\), CO, \(\mathrm{H}_{2} \mathrm{O}\), and \(\mathrm{N}_{2}\) only. Determine the temperature of the exiting products, in K. Compare with the results of Example 13.8 and comment.

Ethane (\(\mathrm{C}_{2} \mathrm{H}_{6}\)) gas at \(77^{\circ} \mathrm{F}\), 1 atm enters a well-insulated reactor operating at steady state and burns completely with air entering at \(240^{\circ} \mathrm{F}\), 1 atm. Determine the temperature of the products, in \({ }^{\circ} \mathrm{C}\). Neglect kinetic and potential energy effects.

For each of the following fuels, plot the adiabatic flame temperature, in K, versus percent excess air for complete combustion in a combustor operating at steady state. The reactants enter at \(25^{\circ} \mathrm{C}\), 1 atm. (a) carbon. (b) hydrogen (\(\mathrm{H}_{2}\)). (c) liquid octane (\(\mathrm{C}_{8} \mathrm{H}_{18}\)).

Propane gas (\(\mathrm{C}_{3} \mathrm{H}_{8}\)) at \(25^{\circ} \mathrm{C}\), 1 atm enters an insulated reactor operating at steady state and burns completely with air entering at \(25^{\circ} \mathrm{C}\), 1 atm. Plot the adiabatic flame temperature versus percent of theoretical air ranging from 100 to 400%. Why does the adiabatic flame temperature vary with increasing combustion air?

Hydrogen (\(\mathrm{H}_{2}\)) at \(77^{\circ} \mathrm{F}\), 1 atm enters an insulated reactor operating at steady state and burns completely with x% of theoretical air entering at \(77^{\circ} \mathrm{F}\) 1 atm. Plot the adiabatic flame temperature for x ranging from 100 to 400%.

Methane gas (\(\mathrm{CH}_{4}\)) at \(25^{\circ} \mathrm{C}\), 1 atm enters an insulated reactor operating at steady state and burns completely with x% of theoretical air entering at \(25^{\circ} \mathrm{C}\), 1 atm. Plot the adiabatic flame temperature for x ranging from 100 to 400%.

Liquid octane (\(\mathrm{C}_{8} \mathrm{H}_{18}\)) at \(25^{\circ} \mathrm{C}\), 1 atm enters an insulated reactor operating at steady state and burns completely with air entering at \(227^{\circ} \mathrm{C}\), 1 atm. The combustion products exit the reactor at \(1127^{\circ} \mathrm{C}\). Determine the percent excess air used. Neglect kinetic and potential energy effects.

Repeat Problem 13.71 if the fuel and air enter at \(77^{\circ} \mathrm{F}\), 1 atm and the products exit at \(1500^{\circ} \mathrm{F}\).

Methane (\(\mathrm{CH}_{4}\)) at \(77^{\circ} \mathrm{F}\), 1 atm enters the combustor of a gas turbine power plant operating at steady state and burns completely with air entering at \(400^{\circ} \mathrm{F}\). Owing to metallurgical limitations, the temperature of the combustion products exiting the combustor to the turbine can be no higher than \(1600^{\circ} \mathrm{F}\). Determine the percent excess air that allows this constraint to be met. Neglect heat transfer from the combustor and kinetic and potential energy effects.

Methane (\(\mathrm{CH}_{4}\)) at \(77^{\circ} \mathrm{F}\) enters the combustor of a gas turbine power plant operating at steady state and burns completely with air entering at \(400^{\circ} \mathrm{F}\). The temperature of the products of combustion flowing from the combustor to the turbine depends on the percent excess air for combustion. Plot the percent excess air versus combustion product temperatures ranging from 1400 to \(1800^{\circ} \mathrm{F}\). There is no significant heat transfer between the combustor and its surroundings, and kinetic and potential energy effects can be ignored.

Air enters the compressor of a simple gas turbine power plant at \(70^{\circ} \mathrm{F}\), 1 atm, is compressed adiabatically to \(40 \mathrm{lbf} / \mathrm{in} .^{2}\), and then enters the combustion chamber where it burns completely with propane gas (C3H8) entering at \(77^{\circ} \mathrm{F}\), \(40 \mathrm{lbf} / \mathrm{in} .^{2}\)and a molar flow rate of 1.7 lbmol/h. The combustion products at \(1340^{\circ} \mathrm{F}\), \(40 \mathrm{lbf} / \mathrm{in} .^{2}\) enter the turbine and expand adiabatically to a pressure of 1 atm. The isentropic compressor efficiency is 83.3% and the isentropic turbine efficiency is 90%. Determine at steady state (a) the percent of theoretical air required. (b) the net power developed, in horsepower.

A mixture of gaseous octane (\(\mathrm{C}_{8} \mathrm{H}_{18}\)) and 200% of theoretical air, initially at \(25^{\circ} \mathrm{C}\), 1 atm, reacts completely in a rigid vessel. (a) If the vessel were well-insulated, determine the temperature, in \({ }^{\circ} \mathrm{C}\), and the pressure, in atm, of the combustion products. (b) If the combustion products were cooled at constant volume to \(25^{\circ} \mathrm{C}\), determine the final pressure, in atm, and the heat transfer, in kJ per kmol of fuel.

Methane gas (\(\mathrm{CH}_{4}\)) reacts completely with the theoretical amount of oxygen (\(\mathrm{O}_{2}\)) in a piston-cylinder assembly. Initially, the mixture is at \(77^{\circ} \mathrm{F}\), 1 atm. If the process occurs at constant pressure and the final volume is 1.9 times the initial volume, determine the work and the heat transfer, each in Btu per lbmol of fuel.

A \(5 \times 10^{-3} \mathrm{kg}\) sample of liquid benzene (\(\mathrm{C}_{6} \mathrm{H}_{6}\)) together with 20% excess air, initially at \(25^{\circ} \mathrm{C}\) and 1 atm, reacts completely in a rigid, insulated vessel. Determine the temperature, in \({ }^{\circ} \mathrm{C}\), and the pressure, in atm, of the combustion products.

Carbon enters a well-insulated reactor at \(\25^{\circ} \mathrm{C}\), 1 atm and reacts completely with excess air entering at 500 K, 1 atm. The products exit at 1200 K, 1 atm. For operation at steady state and ignoring kinetic and potential energy effects, determine (a) the percent excess air, (b) the rate of entropy production, in kJ/K per kmol of carbon.

Pentane (\(\mathrm{C}_{5} \mathrm{H}_{12}\)) gas enters a well-insulated reactor at \(25^{\circ} \mathrm{C}\), 1.5 atm and reacts completely with excess air entering at 500 K, 1.5 atm. The products exit at 1800 K, 1.5 atm. For operation at steady state and ignoring kinetic and potential energy effects, determine (a) the percent excess air, (b) the rate of entropy production, in kJ/K per kmol of pentane.

Ethylene (\(\mathrm{C}_{2} \mathrm{H}_{4}\)) gas enters a well-insulated reactor and reacts completely with 400% of theoretical air, each at \(25^{\circ} \mathrm{C}\), 2 atm. The products exit the reactor at 2 atm. For operation at steady state and ignoring kinetic and potential energy effects, determine (a) the balanced reaction equation, (b) the temperature, in K, at which the products exit, (c) the rate of entropy production, in kJ/K per kmol of ethylene.

Methane (\(\mathrm{CH}_{4}\)) at \(77^{\circ} \mathrm{F}\), 1 atm enters an insulated reactor operating at steady state and burns completely with air entering in a separate stream at \(77^{\circ} \mathrm{F}\), 1 atm. The products of combustion exit as a mixture at 1 atm. For the reactor, determine the rate of entropy production, in Btu/R per lbmol of methane entering, for combustion with (a) the theoretical amount of air. (b) 200% of theoretical air. Neglect kinetic and potential energy effects.

A gaseous mixture of butane (\(\mathrm{C}_{4} \mathrm{H}_{10}\)) and 80% excess air at \(25^{\circ} \mathrm{C}\), 3 atm enters a reactor operating at steady state. Complete combustion occurs and the products exit as a mixture at 1200 K, 3 atm. Refrigerant 134a with a mass flow rate of 5 kg/s enters an outer cooling jacket as saturated liquid and exits the jacket as saturated vapor, each at \(25^{\circ} \mathrm{C}\). No stray heat transfer occurs from the outside of the jacket, and kinetic and potential energy effects are negligible. Determine for the jacketed reactor (a) the molar flow rate of the fuel, in kmol/s. (b) the rate of entropy production, in kW/K. (c) the rate of exergy destruction, in kW, for \(T_{0}=25^{\circ} \mathrm{C}\).

Liquid ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)) at \(25^{\circ} \mathrm{C}\), 1 atm enters a reactor operating at steady state and burns completely with 130% of theoretical air entering in a separate stream at \(25^{\circ} \mathrm{C}\), 1 atm. Combustion products exit at \(227^{\circ} \mathrm{C}\), 1 atm. Heat transfer from the reactor takes place at an average surface temperature of \(127^{\circ} \mathrm{C}\). Determine (a) the rate of entropy production within the reactor, in kJ/K per kmol of fuel, (b) the rate of exergy destruction within the reactor, in kJ per kmol of fuel. Kinetic and potential energy effects are negligible. Let \(T_{0}=25^{\circ} \mathrm{C}\).

A gaseous mixture of ethane (\(\mathrm{C}_{2} \mathrm{H}_{6}\)) and the theoretical amount of air at \(25^{\circ} \mathrm{C}\), 1 atm enters a reactor operating at steady state and burns completely. Combustion products exit at \(627^{\circ} \mathrm{C}\), 1 atm. Heat transfer from the reactor takes place at an average surface temperature of \(327^{\circ} \mathrm{C}\). Determine (a) the rate of entropy production within the reactor, in kJ/K per kmol of fuel, (b) the rate of exergy destruction within the reactor, in kJ per kmol of fuel. Kinetic and potential energy effects are negligible. Let \(T_{0}=25^{\circ} \mathrm{C}\).

Determine the change in the Gibbs function, in kJ per kmol of methane, at \(25^{\circ} \mathrm{C}\), 1 atm for \(\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}\), using (a) Gibbs function of formation data. (b) enthalpy of formation data, together with absolute entropy data.

Determine the change in the Gibbs function, in Btu per lbmol of hydrogen, at \(77^{\circ} \mathrm{F}\), 1 atm for \(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\), using (a) Gibbs function of formation data. (b) enthalpy of formation data, together with absolute entropy data.

Streams of methane (\(\mathrm{CH}_{4}\)) and oxygen (\(\mathrm{O}_{2})), each at \(25^{\circ} \mathrm{C}\), 1 atm, enter a fuel cell operating at steady state. Streams of carbon dioxide and water exit separately at \(25^{\circ} \mathrm{C}\), 1 atm. If the fuel cell operates isothermally at \(25^{\circ} \mathrm{C}\), 1 atm, determine the maximum theoretical work that it can develop, in kJ per kmol of methane. Ignore kinetic and potential energy effects.

An inventor has developed a device that at steady state takes in liquid water at \(25^{\circ} \mathrm{C}\), 1 atm with a mass flow rate of 4 kg/h and produces separate streams of hydrogen (\(\mathrm{H}_{2}\)) and oxygen (\(\mathrm{O}_{2}\)), each at \(25^{\circ} \mathrm{C}\), 1 atm. When the device operates isothermally at \(25^{\circ} \mathrm{C}\), the inventor says it requires an electricity input of 237,180 kJ per kmol of hydrogen produced. Heat transfer with the surroundings occurs, but kinetic and potential energy effects can be ignored. Evaluate the inventor’s claim.

As shown in Fig. P13.90, coal with a mass analysis of 88% C, 6% H, 4% O, 1% N, 1% S enters a reactor where it burns with the theoretical amount of air to give a gas stream consisting of \(\mathrm{CO}_{2}\), \(\mathrm{H}_{2} \mathrm{O}\), \(\mathrm{N}_{2}\), \(\mathrm{SO}_{2}\). After the gas stream provides heating in an industrial furnace, it is directed at \(25^{\circ} \mathrm{C}\), 1 atm to a cleanup device operating at steady state that removes the \(\mathrm{CO}_{2}\) and \(\mathrm{SO}_{2}\), each in a separate stream. The remainder is discharged to the atmosphere. Each of these three streams exits the device at \(25^{\circ} \mathrm{C}\), 1 atm, heat transfer to the surroundings occurs at \(25^{\circ} \mathrm{C}\), and the effects of kinetic and potential energy are negligible. Determine the minimum theoretical work input required by any such cleanup device, in kJ per kg of coal entering the reactor. Why is a work input required?

Applying Eq. 13.36 for (a) carbon, (b) hydrogen (\(\mathrm{H}_{2}\)), (c) methane, (d) carbon monoxide, (e) nitrogen (\(\mathrm{N}_{2})), (f) oxygen (\(\mathrm{O}_{2}\)), and (g) carbon dioxide, determine the chemical exergy, in kJ/kg, relative to the following environment in which the gas phase obeys the ideal gas model:

The accompanying table shows an environment consisting of a gas phase and a condensed water phase. The gas phase forms an ideal gas mixture. (a) Show that the chemical exergy of the hydrocarbon \(\mathrm{C}_{a} \mathrm{H}_{b}\) can be determined as \(\begin{aligned} \overline{\mathrm{e}}^{\mathrm{ch}}= & {\left[\bar{g}_{\mathrm{F}}+\left(\mathrm{a}+\frac{\mathrm{b}}{4}\right) \bar{g}_{\mathrm{O}_{2}}-\mathrm{a} \bar{g}_{\mathrm{CO}_{2}}\right.} \\ & \left.-\frac{\mathrm{b}}{2} \bar{g}_{\mathrm{H}_{2} \mathrm{O}(\mathrm{l})}\right]+\bar{R} T_{0} \ln \left[\frac{\left(y_{\mathrm{O}_{2}}^{\mathrm{e}}\right)^{\mathrm{a}+\mathrm{b} / 4}}{\left(y_{\mathrm{CO}_{2}}^{\mathrm{e}}\right)^{\mathrm{a}}}\right] \end{aligned}\) (b) Using the result of part (a), repeat parts (a) through (c) of Problem 13.91.

Justify the use of Eq. 13.36 for liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}\), and liquid ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\), and apply it to evaluate the chemical exergy, in kJ/kmol, of each substance relative to the environment of Prob. 13.91. Compare with the respective standard chemical exergy values from Table A-26 (Model II).

Showing all important steps, derive (a) Eqs. 13.41a, b (b) Eqs. 13.44 a, b.

Using data from Tables A-25 and A-26, together with Eq. 13.44b, determine the standard molar chemical exergy, in kJ/kmol, of propane \(\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{~g})\). Compare this value with the standard chemical exergy from Table A-26 (Model II).

Evaluate the total specific flow exergy of water vapor, in kJ/kg, at \(320^{\circ} \mathrm{C}\), 60 bar. Neglect the effects of motion and gravity. Perform calculations relative to the environment of Table A-26 (Model II).

Nitrogen (\(\mathrm{N}_{2}\)) flows through a duct. At a particular location the temperature is 400 K, the pressure is 4 atm, and the velocity is 350 m/s. Assuming the ideal gas model and ignoring the effect of gravity, determine the total specific flow exergy, in kJ/kmol. Perform calculations relative to the environment of Table A-26 (Model II).

Evaluate the total specific flow exergy of an equimolar mixture of oxygen (\(\mathrm{O}_{2}\)) and nitrogen (\(\mathrm{N}_{2}\)), in kJ/kg, at \(227^{\circ} \mathrm{C}\), 1 atm. Neglect the effects of motion and gravity. Perform calculations (a) relative to the environment of Problem 13.91. (b) using data from Table A-26 (Model II).

A mixture of methane gas (\(\mathrm{CH}_{4}\)) and 150% of theoretical air enters a combustion chamber at \(77^{\circ} \mathrm{F}\), 1 atm. Determine the total specific flow exergy of the entering mixture, in Btu per lbmol of methane. Ignore the effects of motion and gravity. Perform calculations (a) relative to the environment of Problem 13.91. (b) using data from Table A-26 (Model II).

A mixture having an analysis on a molar basis of 85% dry air, 15% CO enters a device at \(25^{\circ} \mathrm{C}\), 2.1 atm, and a velocity of 250 m/s. If the mass flow rate is 1.0 kg/s, determine the rate exergy enters, in MW. Neglect the effect of gravity. Perform calculations (a) relative to the environment of Problem 13.91. (b) using data from Table A-26 (Model II).

The following flow rates in lb/h are reported for the exiting syngas (synthesis gas) stream in a certain process for producing syngas from bituminous coal: If the syngas stream is at \(77^{\circ} \mathrm{F}\), 1 atm, determine the rate at which exergy exits, in MW. Perform calculations relative to the environment of Table A-26 (Model II). Neglect the effects of motion and gravity.

Propane (\(\mathrm{C}_{3} \mathrm{H}_{8}\)) gas at \(25^{\circ} \mathrm{C}\), 1 atm and a mass flow rate of 0.67 kg/min enters an internal combustion engine operating at steady state. The fuel burns with air entering at \(25^{\circ} \mathrm{C}\), 1 atm according to \(\begin{array}{l} \mathrm{C}_{3} \mathrm{H}_{8}+4.5\left[\mathrm{O}_{2}+3.76 \mathrm{~N}_{2}\right] \rightarrow 2.7 \mathrm{CO}_{2}+0.3 \mathrm{CO}+3.3 \mathrm{H}_{2} \mathrm{O} \\ +0.7 \mathrm{H}_{2}+16.92 \mathrm{~N}_{2} \end{array}\) The combustion products exit at 1000 K, 1 atm and the rate of energy transfer by heat from the engine is 100 kW. For the hydrogen, cp 29.5 kJ/kmol K. The effects of motion and gravity can be ignored. Using the environment of Table A-26 (Model II), evaluate an exergetic efficiency for the engine.

Liquid octane (\(\mathrm{C}_{8} \mathrm{H}_{18}\)) at \(25^{\circ} \mathrm{C}\), 1 atm and a mass flow rate of 0.57 kg/h enters an internal combustion engine operating at steady state. The fuel burns with air entering the engine in a separate stream at \(25^{\circ} \mathrm{C}\), 1 atm. Combustion products exit at 670 K, 1 atm with a dry molar analysis of 11.4% \(\mathrm{CO}_{2}\), 2.9% CO, 1.6% \(\mathrm{O}_{2}\), and 84.1% \(\mathrm{N}_{2}\). The engine develops power at the rate of 3 kW. Determine (a) the balanced reaction equation. (b) the rate of heat transfer from the engine, in kW. (c) an exergetic efficiency for the engine. Use the environment of Table A-26 (Model II) and neglect the effects of motion and gravity

Carbon at \(25^{\circ} \mathrm{C}\), 1 atm enters an insulated reactor operating at steady state and reacts completely with the theoretical amount of air entering separately at \(25^{\circ} \mathrm{C}\), 1 atm. Combustion products exit at 2460 K, 1 atm. For the reactor, (a) determine the rate of exergy destruction, in kJ per kmol of carbon, and (b) evaluate an exergetic efficiency. Perform calculations relative to the environment of Table A-26 (Model II). Neglect the effects of motion and gravity.

Carbon monoxide (CO) at \(25^{\circ} \mathrm{C}\), 1 atm enters an insulated reactor operating at steady state and reacts completely with the theoretical amount of air entering in a separate stream at \(25^{\circ} \mathrm{C}\), 1 atm. The products exit as a mixture at 2665 K, 1 atm. Determine in kJ per kmol of CO (a) the exergy entering with the carbon monoxide. (b) the exergy exiting with the products. (c) the rate of exergy destruction. Also evaluate an exergetic efficiency for the reactor. Perform calculations relative to the environment of Table A-26 (Model II). Neglect the effects of motion and gravity.

Propane gas (\(\\mathrm{C}_{3} \mathrm{H}_{8}\)) at \(25^{\circ} \mathrm{C}\), 1 atm and a volumetric flow rate of \(0.03 \mathrm{~m}^{3} / \mathrm{min}\) enters a furnace operating at steady state and burns completely with 200% of theoretical air entering at \(25^{\circ} \mathrm{C}\), 1 atm. The furnace provides energy by heat transfer at \(227^{\circ} \mathrm{C}\) for an industrial process and combustion products at \(227^{\circ} \mathrm{C}\), 1 atm for cogeneration of hot water. For the furnace, determine (a) the rate of heat transfer, in kJ/min, and (b) the rate of entropy production, in \(\mathrm{kJ} / \mathrm{K} \cdot \min\). (c) Also devise and evaluate an exergetic efficiency for the furnace relative to the environment of Table A-26 (Model II). Ignore the effects of motion and gravity.

Complete the solution of Example 13.15 by providing details left to the reader for each of the following: (a) Evaluation of \(h_{4}\) and \(s_{4}\), each in the units given in the table. (b) Evaluation of the total flow exergy at state 4 assuming the hypothetical dead state, introduced in note 5 of the solution, where all water formed by combustion is in vapor form only.

Methane gas enters a reactor and burns completely with 140% of theoretical air, each at \(77^{\circ} \mathrm{F}\), 1 atm. Combustion products exit at \(2820^{\circ} \mathrm{R}\), 1 atm. Assuming all water present in the combustion products is a vapor at the dead state and ignoring the effects of motion and gravity, evaluate the total specific flow exergy of the combustion products. Perform calculations relative to the environment of Table A-26 (Model II).

Consider a furnace operating at steady state idealized as shown in Fig. P13.109. The fuel is methane, which enters at \(25^{\circ} \mathrm{C}\), 1 atm and burns completely with 200% theoretical air entering at the same temperature and pressure. The furnace delivers energy by heat transfer at 600 K. Combustion products at 600 K, 1 atm are provided to the surroundings for cogeneration of steam. There are no stray heat transfers, and the effects of motion and gravity can be ignored. Assuming all water present in the combustion products is a vapor at the dead state, determine in kJ per kmol of fuel (a) the exergy entering the furnace with the fuel. (b) the exergy exiting with the products. (c) the rate of exergy destruction. Also devise and evaluate an exergetic efficiency for the furnace and comment. Perform calculations relative to the environment of Table A-26 (Model II).

Figure P13.110 shows a coal gasification reactor making use of the carbon–steam process. The energy required for the endothermic reaction is supplied electrically at a rate of \(7.85 \times 10^{4}\) Btu per lbmol of carbon entering. The reactor operates at steady state, with no stray heat transfers and negligible effects of motion and gravity. Evaluate in Btu per lbmol of carbon entering (a) the exergy entering with the carbon. (b) the exergy entering with the steam. (c) the exergy exiting with the product gas. (d) the exergy destruction within the reactor. Also devise and evaluate an exergetic efficiency for the reactor. Perform calculations relative to the environment of Table A-26 (Model II). Assume all water vapor present in the combustion products is a vapor at the dead state. For the hydrogen produced, \(\bar{c}_{p}=7.1 \mathrm{Btu} / \mathrm{lbmol} \cdot{ }^{\circ} \mathrm{R}\).

Figure P13.111 shows a simple vapor power plant. The fuel is methane that enters at \(77^{\circ} \mathrm{F}\), 1 atm and burns completely with 200% theoretical air entering at \(77^{\circ} \mathrm{F}\), 1 atm. Steam exits the steam generator at \(900^{\circ} \mathrm{F}\), \(500 \mathrm{lbf} / \mathrm{in} ^{2}\) The vapor expands through the turbine and exits at \(1 \mathrm{lbf} / \mathrm{in} .^{2}\), and a quality of 97%. At the condenser exit, the pressure is 1 lbf/in.2 and the water is a saturated liquid. The plant operates at steady state with no stray heat transfers from any plant component. Pump work and the effects of motion and gravity are negligible. Determine (a) the balanced reaction equation. (b) the vapor mass flow rate, in lb per lbmol of fuel. (c) the cooling water mass flow rate, in lb per lbmol of fuel. (d) each of the following, expressed as a percent of the exergy entering the steam generator with the fuel, (i) the exergy exiting with the stack gases, (ii) the exergy destroyed in the steam generator, (iii) the power developed by the turbine, (iv) the exergy destroyed in the turbine, (v) the exergy exiting with the cooling water, (vi) the exergy destroyed in the condenser. Base exergy values on the environment of Table A-26 (Model II) and assume all water present in the combustion products is a vapor at the dead state.

For psychrometric applications such as those considered in Chap. 12, the environment often can be modeled simply as an ideal gas mixture of water vapor and dry air at temperature \(T_{0}\) and pressure \(p_{0}\). The composition of the environment is defined by the dry air and water vapor mole fractions \(y_{\mathrm{a}}^{\mathrm{e}}, y_{\mathrm{v}}^{\mathrm{e}}), respectively. (a) Show that relative to such an environment the total specific flow exergy of a moist air stream at temperature T and pressure p with dry air and water vapor mole fractions \(y_{a}\) and \(y_{v}\), respectively, can be expressed on a molar basis as \(\begin{aligned} \overline{\mathrm{e}}_{\mathrm{f}}= & T_{0}\left\{( y _ { \mathrm { a } } \overline { c } _ { p \mathrm { a } } + y _ { \mathrm { v } } \overline { c } _ { p \mathrm { v } } ) \left[\left(\frac{T}{T_{0}}\right)\right.\right. \\ & \left.\left.-1-\ln \left(\frac{T}{T_{0}}\right)\right]+\bar{R} \ln \left(\frac{p}{p_{0}}\right)\right\} \\ & +\bar{R} T_{0}\left[y_{\mathrm{a}} \ln \left(\frac{y_{\mathrm{a}}}{y_{\mathrm{a}}^{\mathrm{e}}}\right)+y_{\mathrm{v}} \ln \left(\frac{y_{\mathrm{v}}}{y_{\mathrm{v}}^{\mathrm{e}}}\right)\right] \end{aligned}\) where \(\bar{c}_{p \mathrm{a}} \text { and } \bar{c}_{p \mathrm{v}}\) denote the molar specific heats of dry air and water vapor, respectively. Neglect the effects of motion and gravity. (b) Express the result of part (a) on a per unit mass of dry air basis as \(\begin{aligned} \overline{\mathrm{e}}_{\mathrm{f}}= & T_{0}\left\{( y _ { \mathrm { a } } \overline { c } _ { p \mathrm { a } } + y _ { \mathrm { v } } \overline { c } _ { p \mathrm { v } } ) \left[\left(\frac{T}{T_{0}}\right)\right.\right. \\ & \left.\left.-1-\ln \left(\frac{T}{T_{0}}\right)\right]+\bar{R} \ln \left(\frac{p}{p_{0}}\right)\right\} \\ & +\bar{R} T_{0}\left[y_{\mathrm{a}} \ln \left(\frac{y_{\mathrm{a}}}{y_{\mathrm{a}}^{\mathrm{e}}}\right)+y_{\mathrm{v}} \ln \left(\frac{y_{\mathrm{v}}}{y_{\mathrm{v}}^{\mathrm{e}}}\right)\right] \end{aligned}\) where \(R_{\mathrm{a}}=\bar{R} / M_{\mathrm{a}} \text { and } \widetilde{\omega}=\omega M_{\mathrm{a}} / M_{\mathrm{v}}=y_{\mathrm{v}} / y_{\mathrm{a}}\).

For each of the following, use the result of Problem 13.112(a) to determine the total specific flow exergy, in kJ/kg, relative to an environment consisting of moist air at \(20^{\circ} \mathrm{C}, 1 \mathrm{~atm}, \phi=100 \%\) \(\begin{array}{l}\text{(a) moist air at } 20^{\circ} \mathrm{C}, 1 \mathrm{~atm}, \phi=90 \% \text{.}\\\text{(b) moist air at } 20^{\circ} \mathrm{C}, 1 \mathrm{~atm}, \phi=50 \% \text{.}\\\text{(c) moist air at } 20^{\circ} \mathrm{C}, 1 \mathrm{~atm}, \phi=10 \% \text{.}\\\text{(d) moist air at } 20^{\circ} \mathrm{C}, 1 \mathrm{~atm}, \phi=0 \% \text{.}\end{array}\)

Middle school science students may wonder how gasoline powers their family’s car. Prepare a 30-minute presentation suitable for an eighth-grade science class to explain the basic operation of a spark-ignition engine while touching on relevant chemical reactions and emission concerns. Include instructional aids and a group activity to enhance your presentation.

Municipal solid waste (MSW), often called garbage or trash, consists of the combined solid waste produced by homes and workplaces. In the United States, a portion of the annual MSW accumulation is burned to generate steam for producing electricity, to heat buildings and water, and for other uses, while several times as much MSW is buried in sanitary landfills. Investigate these two MSW disposal approaches. For each approach, prepare a list of at least three advantages and three disadvantages, together with brief discussions of each advantage and disadvantage. Report your findings in a PowerPoint presentation suitable for a community planning group.

As shown in Fig. P13.3D, the combustion products of two diesel engines, each generating electricity at a rate of 8900 kW, provide energy by heat transfer to a heat-recovery power cycle as the combustion products cool from \(350^{\circ} \mathrm{C}\) to a temperature no less than \(130^{\circ} \mathrm{C}\). A preliminary study has identified two types of power cycles suited for such duty: an Organic Rankine Cycle (ORC) and a Kalina Cycle. Of these cycle types, determine which technology is the better option thermodynamically, including identification of a working fluid if an ORC is selected. Fully document the analyses supporting your choice of technology. Report your findings in a PowerPoint presentation suitable for a technical audience.

A proposed simple gas turbine will produce power at a rate of 0.5 MW by burning fuel with 200% theoretical air in the combustor. Air temperature and pressure at the compressor inlet are 298 K and 100 kPa, respectively. Fuel enters the combustor at 298 K, while products of combustion consisting of \(\mathrm{CO}_{2}\), \(\mathrm{H}_{2} \mathrm{O}\), \(\mathrm{O}_{2}\), and \(\mathrm{N}_{2}\) exit the combustor with no significant change in pressure. Metallurgical considerations require the turbine inlet temperature to be no greater than 1500 K. Products of combustion exit the turbine at 100 kPa. The compressor has an isentropic efficiency of 85%, while the turbine isentropic efficiency is 90%. Three fuels are being considered: methane (\(\mathrm{CH}_{4}\)), ethylene (\(\mathrm{C}_{2} \mathrm{H}_{4}\)), and ethane (\(\mathrm{C}_{2} \mathrm{H}_{6}\)). With the aim of minimizing fuel use, recommend a fuel, turbine inlet temperature, and compressor pressure ratio for the gas turbine. Summarize your findings in a report supported by well-documented sample calculations and a full discussion of the thermodynamic modeling used.

Many utilities are converting power plants from coal to alternative fuels due to economic and environmental considerations. Conduct a case study of a power plant in your geographic region that has converted or is planning to convert from coal to an alternative fuel. Provide a schematic of the coal-based system and the alternative fuel-based system and describe pertinent features of each. Investigate the physical plant changes with associated costs required to accommodate the new fuel, and the impact of the fuel change on system performance and operational cost. Summarize your findings in a PowerPoint presentation suitable for your class.

Identify and research a fuel cell system for combined heat and power integrated with a building in your locale. Describe each component in the fuel cell system and create a schematic of the system to include fuel cell stack, its auxiliary components, and its integration with the building to provide electricity and heating. Contact the building supervisor to identify any installation, operational, and/or maintenance issues. Estimate total costs (components, installation, and annual fuel and operating costs) for the fuel cell system and compare to the prior system’s cost, assuming the same annual electricity and heating requirements. Summarize your findings in a PowerPoint presentation.

In 2012, the U.S. Environmental Protection Agency released the Mercury and Air Toxics Standards. These standards include regulations limiting mercury emissions from coal-fired power plants. Other hazardous pollutants are also curtailed, including lead, arsenic, hydrogen chloride, and hydrogen fluoride. Further, the standards establish maximum achievable control technology (MACT) limits for many such substances. Soon after the release some in the business community raised concerns about economic hardships that could result from implementation of the standards. Investigate the pros and cons of these standards and place your conclusions in the form of an op-ed (opinion-editorial) article for a local newspaper. Observe established practices for preparing op-ed articles and avoid technical jargon. While op-eds are aimed at a general audience, they should be supported with evidence.

The chemical exergies of common hydrocarbons \(\mathrm{C}_{a} \mathrm{H}_{b}\) can be represented in terms of their respective lower heating value, \(\overline{\text { LHV }}\), by an expression of the form \(\frac{\overline{\mathrm{e}}^{\mathrm{ch}}}{(\overline{\mathrm{LHV}})}=c_{1}+c_{2}(\mathrm{~b} / \mathrm{a})-c_{3} / \mathrm{a}\) where \(c_{1}\), \(c_{2}\), and \(c_{3}\) are constants. Evaluate the constants to obtain an expression applicable to the gaseous hydrocarbons of Table A-26 (Model II).

As shown in Fig. P13.9D, a gaseous fuel of the form \(\mathrm{C}_{a} \mathrm{H}_{b}\) enters a well-insulated reactor at \(25^{\circ} \mathrm{C}\), 1 atm and reacts completely with the theoretical amount of air also entering at \(25^{\circ} \mathrm{C}\), 1 atm. Products of combustion exit at \(T_{P}\), 1 atm. Ignoring the effects of motion and gravity, evaluate the exergy destruction within the reactor, in kJ per kmol of fuel, for \(\mathrm{H}_{2} \mathrm{CH}_{4}, \mathrm{C}_{2} \mathrm{H}_{6}, \mathrm{C}_{3} \mathrm{H}_{8}, \mathrm{C}_{4} \mathrm{H}_{10} \text { and } \mathrm{C}_{5} \mathrm{H}_{12}\). Basing exergy values on the environment of Table A-26 (Model II), determine in each case the percentage of the fuel exergy destroyed upon combustion. Plot the percentages versus b, the number of hydrogen atoms per molecule, and interpret the plot. In a memorandum summarize findings and conclusions.

Coal mining operations in certain regions of the United States have created vast amounts of waste coal known as culm. Some power plants have been built near culm banks to generate electricity from this waste resource. A particular culm sample has the following ultimate analysis: 44.1% C, 2.9% H, 16% O, 0.5% N, and 0.5% S. The higher heating value including moisture and ash is 15,600 kJ/kg; the higher heating value on a dry and ash-free basis is 32,600 kJ/kg. Estimate the chemical exergy of this sample, in kJ/kg. For comparison, also determine the chemical exergy value of anthracite coal. Investigate the advantages and disadvantages of using culm instead of coal in power plants. Write a report summarizing your findings, including a comparison of the chemical exergy values obtained, sample calculations, and at least three references.

Shown in Fig. P13.11D is the schematic of a cogeneration system providing both power and steam. Develop a full exergy accounting of the exergy entering with the fuel. Evaluate the exergetic efficiency of each system component and the overall cogeneration system. Using these results, identify tweaks to the given system promising greater overall exergetic efficiency. Present your analyses, results, and recommendations in a technical article adhering to ASME standards with at least three references. The six-point engineering model to follow, which is based on a previous concept development design effort, gives key assumptions and data. Additional assumptions may be necessary. (1) The cogeneration system operates at steady state. The effects of motion and gravity at the numbered states can be ignored. (2) Air enters the compressor at \(25^{\circ} \mathrm{C}\), 1 atm. These values correspond to the temperature and pressure of the exergy reference environment of Table A-26 (Model II), which is assumed. The molar analysis of the air is 77.48% \(\mathrm{N}_{2}\); 20.59% \(\mathrm{O}_{2}\); 0.03% \(\mathrm{CO}_{2}\); 1.90% \(\mathrm{H}_{2} \mathrm{O}\)(g). The molecular weight is 28.649. The air forms an ideal gas mixture. (3) Natural gas, regarded to be methane modeled as an ideal gas, is injected into the combustor at \(25^{\circ} \mathrm{C}\), 12 bar. Combustion with excess air is complete. The combustion products form an ideal gas mixture. The pressure drop through the combustor is 5%. Heat transfer from the combustor is 2% of the fuel lower heating value. All other system components operate adiabatically. (4) For the regenerator there is a 5% pressure drop on the air side and a 3% pressure drop on the combustion product side. Preheated compressed air exits the regenerator at 850 K. (5) For the heat-recovery steam generator, feedwater enters at \(25^{\circ} \mathrm{C}\), 20 bar and saturated vapor exits at 20 bar with a mass flow rate of 14 kg/s. A pressure drop of 5% occurs on the combustion product side and the combustion products exit at 1 atm. (6) The compressor pressure ratio is 10. The isentropic compressor and turbine efficiencies are each 86%. The temperature at the turbine inlet is 1520 K. The net power developed is 30 MW.